Probability question on seating arrangements

[jackbauer]

Hi people, was wondering if someone could help me with this question. n men and m women are seated at a round table with n+m chairs. find the probability that a man amongst the n men has a woman seated immediately to his right? Find also the probability that a woman in the m women has a man either side of her? I think that the total sample space of possible arrangements from combinatorics is (n+m-1)! but i don't know how to proceed from here?Anyone got any hints?
Thanks
Jack

 

[D H]

Jack, you are making too much of this problem. It's easy. Since the table is round, everyone at the table has someone to their right and someone else to their left. No nasty endpoint conditions exist. You are asked about the gender of the person sitting in an adjacent seat. Those seats are all you need to consider. No combinatorics are needed.